Algebra 2 Chapter 7 Review
NO CALCULATOR SECTION
For #1-2, expand each expression completely.
x 4 y5
1.) log3
z 2 p3
2.) log 4
a6 b
 d  4 3
For #3-4, condense each expression into a single logarithm:
3.) 3ln 3  2 ln y  4 ln z
1
4.) 2 log 4 5  3log 4 2  log 4 9
2
For #5-8, find the value of x.
5.) log16 8  x
6.) 4 x  162 x1
7.) log 2 3x  log 2 6  4
8.) log 4 5  log 4 x  log 4 60
9.) Graph. Find the requested information
below:
x 1
1
f  x  3   4
2
Parent: _______
y
10
9
8
7
6
Shift: ______________
5
4
3
2
1
x
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
Domain: _______, Range: ________
Equation of Asymptote: __________
-8
-9
-10
1 2 3 4 5 6 7 8 9 10
CALCULATOR SECTION
For #9-20, solve each equation. Where necessary, round your answer to 4 decimal places. Be sure
to check for extraneous solutions (solutions that don’t work in the original problem)!
10.) 3log 7 4  2 log 7 b
11.) log 4 x  log 4 (2 x  3)  log 4 2
12.) 8  105 x 4  35
8
13.) log5 64  log5  log5 2  log5 4 x
3
14.) 6 ln x  18
15.) 8e4 x  96
16.) log x  log( x  3)  1
17.) log 2 (12 x  21)  log 2 ( x 2  3)  2
18.) You deposit $800 in an account that pays 5.2% annual interest. Find the balance after seven years
if the interest is compounded:
A: Monthly
B: Daily
C. Continuously
19.) You have bought a new car for $24,000. The value y of the car decreases by 16% each year.
A.) Write an exponential decay model for the value of the car.
B.) Use the equation/model to estimate the value of the car after five years.
C.) Use the equation/model to estimate when the car will have a value of $18,000.